Error-floor mitigated and repetitive turbo coding communication system

ABSTRACT

The turbo coding system combines: a) repetitive turbo encoder bit partitioning and decoder bit deletion; with b) error-floor mitigating encoder non-flushing the second constituent encoder with the second a-posteriori probability (APP) decoder starting backward recursion from any possible states as a powerful improvement to conventional turbo coding. The repetitive turbo encoding process repeats the bits of the systematic root sequence and appends flushing sequence prior to interleaving and encoding by the second constituent turbo encoder for providing an interleaved repetitive second encoded output for turbo decoding. The error-floor mitigating turbo encoding process does not flush the second constituent encoder to the zero ending state so that turbo decoding forward recursion may be end in any possible state and backward recursion may start from any possible state to avoid potential mismatches between the forward and backward recursions. The modified a posterior probability second decoder initializes the beginning state metric of the backward recursion with the ending state metric of the forward recursion. The two processes provide significant bit error rate improvement. Iterative decoding provides iterative results that are subject to majority voting selection for improved estimations of the decoded systematic data sequence.

STATEMENT OF GOVERNMENT INTEREST

The invention was made with Government support under contractF04701-93-C-0094 by the Department of the Air Force. The U.S. Governmenthas certain rights in the invention.

REFERENCE TO RELATED APPLICATION

The present application is related to applicant's application entitled"Error-Floor Mitigating Turbo Code Communication Method" Ser. No.:09/182,447, filed Oct. 29, 1998, by the same inventor.

The present application is related to applicant's application entitled"Repetitive Turbo Coding Communication Method" Ser. No.: 09/182,445,filed Oct. 29, 1998, by the same inventor.

FIELD OF THE INVENTION

The invention relates to the field of channel encoding and decoding forthe communication of data across a noisy channel. More particularly, theinvention relates to turbo encoding and decoding methods and systems.

BACKGROUND OF THE INVENTION

Conventional Reed-Solomon and convolutional coding have been usedtogether to correct both burst and random errors, respectively, in acontinuous stream of convolved data bits. Conventional convolutionalencoders use an interleaver to interleave code bits over a larger timeperiod for translating uncorrectable burst errors into correctablerandom errors. However, in low bit energy to noise power spectraldensity Eb/No applications, conventional convolutional coding errorcorrection often does not meet system required bit error rates (BER).One technique for improving error rates is to repeat the transmission ofa channel bit several times. A bit is partitioned into several identicalbits and transmitted. However, this bit partitioning disadvantageouslyincreases the effective transmission rate and may not effectivelyimprove the BER in low bit energy to noise power spectral density Eb/Noapplications.

In recent years, the newly developed turbo code method has beendemonstrated to be a very powerful tool for forward error correction ofcorrupted data communicated across noisy data channels. Turbo coding canprovide significant coding gain within a fraction of 1 dB from thetheoretical Shannon limit. This coding gain presents a promising futurefor power limited communication systems, such as a satellitecommunication system. The turbo code can provide significant coding gainat low Eb/No. In comparison with the commonly used concatenatedReed-Solomon convolutional codes, an additional coding gain can beachieved. Transfer function bound techniques have been studied toanalytically compute the upper bound of the BER performance of aparallel concatenated convolutional code with a maximum likelihooddecoder based on a trellis diagram and uniform interleaving. It has beenshown that the simulated turbo code performance merge to this boundasymptotically. Therefore, this bound has been used to indicate wherethe error floor of a turbo code is located.

Turbo coding is a block code process using a transmitting turbo encoderand a receiving turbo decoder. In the case of continuous datatransmission, turbo coding requires that the data stream be packetizedinto blocks for processing an entire message by blocks of N data bits.The turbo encoder provides systematic data bits uk and includes a firstand a second constituent convolutional recursive encoders respectivelyproviding e1 and e2 outputs of code bits. The first encoder operates onthe systematic data bits providing the e1 output of code bits. Anencoder interleaver provides interleaved systematic data bits then fedinto the second encoder. The second encoder operates on the interleaveddata bits providing the e2 output of code bits. The data uk and codebits e1 and e2 are concurrently processed and communicated in blocks ofdigital bits.

The conditional probability that the constituent encoder generates acodeword of weight dc given an information sequence of weight i andblock size N can be expressed as pc(dc.linevertsplit.i)=t(N,i,dc)/C(N,i), where C(N,i) is the number of combinations ofN bits taken i at a time, and t(N,i,d) is the number of codewords ofweight d, which is simply the coefficient of the term L^(N) *I^(i)*D^(d) of the transfer function T(L,I,D) of the constituent code with *being multiplication. Based on the assumption of uniform interleaving,the conditional probability of having a turbo codeword with a totalweight of d given an information sequence of weight i and block size Nis p(d.linevert split.i)=p0(d0.linevert split.i)*pc1(d1.linevertsplit.i)*pc2(d2.linevert split.i) where d=d0+d1+d2 with d0 being theweight of the systematic fragment of the codeword, d1 and d2 beingweights of the encoded fragments corresponding to the first and secondconstituent encoder, respectively. The term p0(d0.linevert split.i) is adelta function d(i,d0), and pc1(d1.linevert split.i) and pc2(d2.linevertsplit.i) are given by the pc(dc.linevert split.i) equation. Applyingwell-known union bound techniques, the probability of bit error Pb forturbo codes can be expressed by a Pb summation equation of Pb being lessthan the summation from i=1 to N of (i/N)*C(N,i)*Ed.linevertsplit.i[Q[sqrt(2*d*(Es/No))]], where the conditional expectationEd.linevert split.i(.) is over the probability distribution functiongiven by the p(d.linevert split.i) equation and Q(.) is thecomplementary Gaussian distribution function with zero mean and unitvariance, sqrt is the square root function, Es=R*Eb with R being thecode rate. Therefore, the structure of the constituent encoder providesthe transfer function T(L,I,D) and, as a result, the asymptotic BERperformance, which can be used to locate the error floor, can beevaluated.

The second interleaver for the second encoder is an essential device forthe turbo code structure. The encoder interleaver is used to increasethe minimum Hamming distance between code words represented by the statetransitions within the trellis diagram. The longer the Hamming distancebetween adjacent code words, the larger an error must be to beuncorrectable. Without this second interleaver, the Hamming weight ofthe combined two code sequences, e1 and e2, is only doubled using twoidentical constituent encoders. With the code rate decreased, theeffectiveness of using concatenation is diminished. However, by uniquelyinterleaving the information systematic sequence that generates theminimum Hamming weight, and generates an interleaved systematic input tothe second constituent encoder, the Hamming weight of the second codesequence e2 can be higher than that of the first code sequence e1.

In order to prevent the processing of a block of information fromaffecting the processing of the next block, the turbo encoder needs tobe flushed at the end of each block. Flushing is the process of enteringrespective sequences of input flushing bits into the constituentencoders so that the contents of the respective shift registers of theencoders become all zeros, to put the encoders in the zero state, at theend of this flushing process. Because the turbo code adopts therecursive convolutional encoders, entering consecutive K-1 zero bits,where K is the constraint length of the code, does not flush the encoderas it does for the conventional nonrecursive convolutional encoder. Theflushing bits for the first encoder are not part of, but are appendedto, the informational root systematic data sequence. A first series ofsystematic tail bits are fed into the first encoder to flush the firstencoder to the zero state as the first encoder generates parity checktail bits, after which, a second series of flushing bits are fed intothe second encoder to flush the second encoder to the zero state whilegenerating second parity check tail bits. Flushing the secondconstituent encoder, in the conventional manner, is to insert mgenerated input flushing bits to clear the contents of the shiftregister to all zeros. At the end of this flushing process, thecorresponding path on the trellis diagram terminates at the all-zerostate for both encoders. The flushing bits are particularly generated toflush the encoders into the zero state.

The first encoder operates on the systematic data and systematic tailbits to provide the first code bits including the first parity checktail bits while the second encoder operates on an interleaved version ofthe systematic data bits only to provide the second code bits and thengenerates the second parity check tail bits as appended to the secondcode bits. At the end of the systematic sequence, a first series offlushing bits is generated and used to flush the first encoder to thezero state as the first encoder generates first parity check tail bitsappended to the first code bits, and concurrently, the first set offlushing bits is appended to the systematic data sequence of data bitsas systematic tail bits, while concurrently, a second set of generatedflushing bits is used to flush the second encoder to the zero stategenerating the second parity check tail bits without interleaving orappending this second set of flushing bits. Flushing of the secondconstituent turbo encoder create a tail effect inherent in block turboencoding and decoding. Flushing of the constituent encoders providesknown ending zero states to which forward recursion ends and from whichbackward recursion begins when estimating the systematic data sequenceduring decoding. The second encoder provides the second parity checktail bits from the second series of flushing bits which, however, arenot appended to the systematic data bits, and hence, the second encoderdoes not have parity check tail bits encoded from the systematic tailbits as does the first encoder. Therefore, a tail effect is created by amismatch between the systematic tail bits and the second encoder paritycheck tail bits. This tail effect does not extend to the first encoderparity check tail bits that were encoded from the systematic tail bits.Consequently, the entire systematic data and tail bit sequence can becompared to the entire string of first code bits for data verification.However, only the root portion of the systematic data sequence can becompared to the root portion of the second code bits, anddisadvantageously the second parity check tail bits can not be comparedto the systematic tail bits for verification. This difference inverification capability results from the tail effect mismatch. Hence,and as a result of the flushing process, there is a difference betweenthe two sets of flushing bits respectively for the first and secondencoders. This tail effect mismatch exists between the first set offlushing systematic tail bits that flush the first encoder to the zerostate and the second set of flushing tail bits that flush the secondconstituent encoder to the zero state. As a result of this tail effectmismatch, the decoder can not compare the systematic tail bits againstthe second parity check tail bits. Such tail effects are a factorcausing the error floor in turbo coding. Flushing of both of theconstituent encoders is conventional practice in the art to terminatethe encoding process to the zero state, but with the resulting errorfloor from the tail effect mismatch. But, a benefit of flushing theencoders to the zero state is that the decoder can take advantage ofsuch known information to assist in the decision-making process fordetermining the systematic data bits. Specifically, the backwardrecursion of the turbo decoding process can start from this known zerostate with a probability of one.

Turbo coding operates on blocks of input data bits dk. The turbo encoderincludes the first and second recursive encoders having respectivelydata inputs and interleaved data inputs for providing respective stringsof code bits e1 and e2, and includes a data channel providing thesystematic unaltered data bits u. The code bits and data bits are usedas branch words extending between states used in a Viterbi searchalgorithm using a trellis state diagram. Each encoder includes anfeedback shift register having a limited number of determined states. Asdata bits or interleaved data bits are fed into the shift register, theencoder jumps among the states depending on the input bits as theencoder generates code bits. The data bits and code bits define possiblebranchwords. The code bits and data bits are transmitted over a noisychannel creating errors in the received code and data bits. At thedecoder, the states and transitional branch words can be depicted usinga trellis diagram upon which a-posteriori probability algorithm isapplied to determine state metric values throughout the trellis diagram,and therefore the most probable transitions between states which thendetermines the data bit and code bits which should have been received soas to enable correction of erroneously received code and data bits. Thea-posteriori probability algorithm can be applied in both forward andbackward recursions using soft metrics based on channel characteristicsand a-priori probabilities of bits being zeros or ones. The encodersstart in the zero state and are flushed at the end of the block of databits to end in the zero state. The a-posteriori probability algorithm isthus applied to known starting and ending states, and, sets of statemetrics between the starting and ending states can be computed basedupon conventional metric computational algorithms.

While the information data sequence, denoted by u, is being fed into thefirst encoder, an encoded sequence of N code bits, denoted by e1, isgenerated accordingly. The flushing systematic tail bits for the firstencoder are appended to the tail of data sequence u, and combined aspart of the systematic sequence uk that is transmitted over the channel.The m=K-1 flushing tail bits are referred to as systematic tail bits,denoted by u*. Associated with these systematic tail bits, the firstencoder generates m parity check tail bits, denoted by e1*, which areappended to the tail of the first encoded sequence e1. Along with thesystematic sequence u;u* the first code sequence e1;e1* is transmittedover the channel. The input sequence to the second constituent encoderis the interleaved version of u, denoted by p(u). The second code bit e2are generated from interleaved data p(u). During the process of flushingthe second encoder, the tail bits e2* are appended to the second codebits, Hence, for each block of N information bits, there are three (N+m)block strings uk=u;u*, e1k=e1;e1*, and e2k=e2;e2* transmitted throughthe noisy communication channel.

The data structures of the input and output sequences for bothconstituent encoders may be plotted as paths on trellis diagrams. Thedata structures of the systematic and code sequences that aretransmitted over a noisy channel are assumed to be corrupted. Theredundancy of the code sequences offers additional information forcorrecting data bit errors. The output data structure for turbo encoderincludes one set of systematic data bits uk and two sets of code bitse1k and e2k providing one set of received systematic data bit sequenceXk and two sets of received code sequences Y1k and Y2k.

A code rate is the ratio of the number of data bits to the number oftransmitted channel symbols. Decreasing the code rate improves the BERperformance. However, for a fixed data rate, decreasing the code rateincreases the transmission symbol rates. Channels are bandwidth limitedand therefore require limited transmission symbol rates. One way of notincreasing the transmission symbol rate while achieving a low code rateperformance is to puncture the transmitted symbols. Puncturing is theprocess of deleting a portion of the transmitted symbols and thepuncturing process is characterized by a puncture pattern used by theturbo encoder. Upon receipt of the transmitted punctured code symbols,the turbo decoder implements a bit insertion process that is the inversefunction of the puncturing process. Bit insertion requires dummy bitsinserted into the received sequence according an insertion pattern aspart of the turbo decoding process. The puncturing and corresponding bitinsertion processes result in a modest degradation of the BERperformance while decreasing the transmission symbol rate to be withinthe acceptable channel bandwidth. Hence, puncturing and bit insertionprocesses are desirable in bandwidth limited applications.

The turbo decoder receives digital bits through a noisy channeltypically communicating modulated analog signals. The noisy channel maycorrupt the transmitted bits uk, e1k and e2k. Typically, a receivedvoltage signal is demodulated into a voltage level and is then assigneda probability based on noisy channel characteristics and bit biasinformation for translating the received analog signals into digitalbits. A communication channel has inherent noise characteristics. Biasinformation is used to describe the a-priori probability of a bit beinga zero or a one. The bias information and the channel noise probabilitydensity function combine to provide channel a-posteriori probabilityestimations. The received digital bits include received systematic databits Xk corresponding to the transmitted data bits uk, and receivedfirst and second code bits Y1k and Y2k corresponding to transmittedfirst code bits e1k and the second code bits e2k code bits,respectively. An information data bit is associated with a probabilityof being a zero or a one. Upon reception, the information bit has aninitial a-priori probability. The bit has an a-priori probability ofbeing a one or a zero for the received soft signal to provide a data bitestimate, and for computing a posteriori bias information.

The turbo decoder includes first and second a-posteriori probability(APP) decoders, a first decoder interleaver, a second decoderinterleaver, an output deinterleaver, a feed back deinterleaver, and ahard limiter. These APP decoders and deinterleavers are connected forproviding inverse functions of the encoders and encoder interleaver. Thefirst and second APP decoders operate in the logarithmic domain. The APPdecoders compute a-posteriori probabilities of the digital bits. The Xand Y1 inputs have the same systematic order and are both inputted intothe first APP decoder providing a first APP output in systematic order.The Y2 input is in an interleaved order by virtue of the encoderinterleaver. The first APP decoder output is fed into a first decoderinterleaver providing a first APP decoder interleaved output ininterleaved order and the input X is also fed into the second decoderinterleaver providing an X interleaved output in interleaved order. Theoutput of the first APP decoder is an input to the first decoderinterleaver providing an interleaved output to the second APP decoder.The second APP decoder provides, in turn, an interleaved biasinformation output that is deinterleaved by the feed back deinterleaverand fed back to the input of the first APP decoder, and provides aninterleaved bit estimate output that is fed to the hard limiter thattranslates bit estimates into hard zero and one bit values. Hence, theturbo decoder includes a turbo feedback loop configuration for feedingback updated bias information. The output of the first APP decoder is aseries of a-posteriori bias information, that is, a bias measurement ofX based upon Y1. The X interleaved output, the first APP decoderinterleaver output, and the Y2 input, all in interleaved order are fedinto a second a-posteriori probability decoder providing the second APPdecoder bias and bit estimate outputs in the interleaved order. One ofthe second APP decoder outputs is a refined APP metric output that isfed into the feedback loop deinterleaver for translating the second APPdecoder bias output into systematic order for feed back into the firstAPP decoder. The feedback metric output and the first APP decoder metricoutput are a measure of the probability of the data X bits being ones orzeros. The second APP decoder provides bias information as a metricoutput for feed back and provides the estimate output that is not fedback to provide an estimate of the bit values. The second APP decoderestimate output is not fed back because it includes the first APPdecoder metric output which should not influence the processing of thefirst APP decoder. The first and second APP decoder independentlyprovides repetitive estimations for respective processing interactions.

At the end of the last iteration of the feedback loop turbo processingthrough the turbo decoder, the second APP decoder estimate output is fedinto the output deinterleaver for generating an estimate output insystematic order for processing through the hard limiter for translatingthe estimates into hard data bit values. The second APP decoder providesan estimate of the systematic data X only at the last iteration. Foreach iteration, the second APP decoder provides a feedback bias metricoutput that is fed back into the first APP decoder. The estimate outputof the second APP decoder is a logarithmic likelihood ratio output. Theestimate output, in systematic order, is fed into a hard limiter fortranslating bit logarithmic likelihood ratios into zero and one bits ofblocks of systematic data bits.

Each APP decoder performs branch and state metric computation during theforward recursion and backward recursion. The process of the forwardrecursion in the first and second APP decoders starts at the all-zerostate with a probability of one, because the first and second encoder isalways initialized at the all-zero state. The backward recursion in thefirst and second APP decoders also always starts from the all-zero statewith a probability of one, because the first or second encoder alwaysterminates at the all-zero state. At the end of the forward and backwardrecursions for each iteration, the first and second decoders performlogarithmic likelihood function calculation to provide the first andsecond decoder bias outputs as well as the second decoder estimateoutput.

The u*tail bits and e1* tail bits are the true matched pairs by virtueof encoding the u*tail bits in the first encoder so that thecorresponding X* and Y1* tail bits can assist each other in determiningdecoded bits during the decoding. For example, if a parity check tailbit in e1* is severely corrupted and the corresponding systematic tailbit in u* is not, the use of X* can be used to correct the corruption ofthe Y1* bit, and vice versa. This is not true for the e2* and u*systematic tail bits because the e2* tail bits were not encoded in thesecond encoder from the u* systematic tail bits. During decoding usingthe e2* second parity check tail bits, arbitrary correspondingsystematic tail bits u* may be used for error correction with aresulting inherent error floor. Specifically, the systematic tail bitsX* cannot be used for decoding in the second APP decoder because the X*tail bits were not used to generate the Y2* tail bits. Using X* fordecoding of the second parity check tail bits will cause unnecessarydecoding errors at the tail portion resulting in the inherent errorfloor.

Therefore, after completing the decoding of the information root portionof Y2k, the systematic input X* is then effectively shut off with the X*systematic tail bit set to zero bit values. The lack of these systematictail bits X* during the decoding of the second code bits Y2 limits theability to correct the corruption of Y2* parity check tail bits andthereby limits the accuracy of the bit estimates creating the errorfloor. As such, decoding errors likely will exist at the tail in theevent that Y2* is corrupted. Such errors may then propagate to theinformation root portion of the systematic sequence Xk. Although theseerrors may be corrected by the first APP decoder in subsequentiterations, the effect of these errors are continuously injected intothe decoding process from one iteration to another.

The turbo code requires that the first and second encoders be flushed atthe end of the information sequence. However, flushing the secondconstituent encoder results in a tail effect, with a mismatch betweenthe second encoder parity check tail bits and the systematic tail bits.This mismatched tail effect of the conventional turbo decoders causesthe two trellis paths of highest probability in the forward and backwardrecursions of the second APP decoder to not merge together at the tailportion of a block. Forward recursions may end at non zero states withthe highest probability and yet backward recursions must start at theall zero states with a probability of one because the second encoder wasflushed to the zero state resulting in a mismatch between the forwardand backward recursions. Mismatches between forward and backwardrecursions is processed in the second APP decoder. When the second APPdecoder decodes the k-th bit based on the likelihood function, whichdepends on forward metrics, backward metrics, and the branch metric atbit time k, this mismatch will cause the decision to wander between theforward and backward recursion paths from one iteration to another. Suchinstability creates some decoding errors in the rear section of the rootdata portion. This tail effect limits the ability of the decoder tocorrect error and hence establishes an inherent error floor during turbodecoding. These and other disadvantages are solved or reduced using theinvention.

SUMMARY OF THE INVENTION

An object of the invention is to provide a modified second a-posterioriprobability (APP) decoder for enabling backward recursion starting fromall possible ending states during turbo decoding.

Another object of the invention is to provide for majority selection ofiterative estimations of systematic data bits estimated by the modifiedsecond APP decoder.

Another object of the invention is to interleave flushing bits withsystematic data bits as an interleaved block input to a second encoderproviding a block of second code bits for reducing the error floor of aturbo encoder-decoder system.

An object of the invention is to reduce the error rate of turbo codecommunication systems.

Another object of the invention is to use bit partitioning of systematicdata bits providing a repetitive encoder input for reducing the errorrate of turbo code communication systems.

The invention is a method for reducing the error rate in turbo coding. Afirst aspect of the invention is to reduce the tail effect that iscreated when flushing the second constituent turbo encoder so that theerror floor is reduced. A second aspect of the invention uses turboencoding bit partitioning for reducing the error rate in turbo codingsystems.

The first aspect of the turbo decoding method is characterized bybackward recursion starting from all possible states. The method avoidsthe mismatch between the ending state of the forward recursion and thebeginning state of the backward recursions in the turbo decodingprocess. Preferably, the second encoder need not be flushed to the zerostate, and preferably uses the systematic tail bits to terminate theencoding of the second encoder so that the turbo encoder can provideboth systematic tail bits and parity check tail bits for both encoderswithout requiring a flushing to the all zero ending state of the secondencoder. The second constituent encoder is not flushed. The method caneliminate the mismatch between the systematic and parity-check tail bitsin the second code bits of the second encoder. Preferably, the secondencoder operates on an interleaved order of the systematic data and tailbits whereas the first encoder operates on a systematic order of thesystematic data and tail bits, hence, both encoders operate on the samesystematic data set having the same number of data bits convenient forblock processing, and both sets of encoder code bits can be used withthe corresponding systematic data bits for data correction.Specifically, the second parity check tail bits can be used incombination with the systematic tail bits in a modified seconda-posteriori probability decoder for better decoding results. Theinvention prevents errors from propagating from the tail portion to theinformation root portion of the block. The method may further reduce thedecoding delay. This method can cause the error rate to converge morerapidly to a final solution.

The method is preferably enhanced by majority selection among harddecisions from all previous iterations of systematic data estimationsduring turbo decoding. During each iteration, the hard limiter providesa hard one or zero value, as a single vote occurrence, for each bit, andafter all of the iterations, the value of zero or one is chosen based onthe higher vote occurrence, for each data bit of the block of N databits. Majority selection of iterative decoding results is used to reducedecoding errors by taking the majority value of ones or zeros of theestimated bits, and in the event of a tie, the bit value of the lastiteration is selected.

The first aspect of the method not only further improves the BERperformance, but may also reduce the decoding delay of the turbodecoder. The method can be used in many types of communication systems,such as, wire communication, wireless communications, and satellitecommunications. The mitigation method is developed to cure the taileffect and simulation results show that the BER continues to drop beyondthe analytical transfer function bound, and shows that there is no errorfloor at all down to a BER range of 1×10E-8.

The second aspect of the invention is repetitive turbo coding forimproving coding gain, and therefore the BER performance, by using bitpartitioning of the systematic sequence prior to encoding in the turboencoder and by using a corresponding inverse bit insertion process inthe turbo decoder. The repetitive turbo coding process increases theminimum Hamming distance for improved coding gain. The repetitive turbocoding method of the second aspect can be used in combination with thefirst aspect of the invention as a comprehensively improved turbo codingcommunication system. These and other advantages will become moreapparent from the following detailed description of the preferredembodiment.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of an error-floor mitigating turbo encoder.

FIG. 2 is a diagram of an error-floor mitigating turbo encoder datastructure of the error-floor mitigating turbo encoder.

FIG. 3 is a block diagram of an error-floor mitigating turbo decoderhaving a modified second a-posteriori probability (APP) decoder withpreferred majority selection.

FIG. 4 is a diagram of an error-floor mitigating turbo encoder datastructure of the error-floor mitigating turbo decoder.

FIG. 5 is a block diagram of a repetitive turbo encoder having a firstand second encoder interleaver with a puncture pattern.

FIG. 6 is a diagram of a repetitive turbo encoder data structure.

FIG. 7 is a diagram of block diagram of a repetitive turbo decoder withbit insertion.

FIG. 8 is a diagram of a repetitive turbo decoder data structure.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

An embodiment of the invention is described with reference to thefigures. FIGS. 1 through 4 depict the first aspect of the inventiondirected to error floor mitigation, and FIGS. 5 through 8 depict thesecond aspect of the invention directed to bit partitioning. Referringto FIGS. 1 and 2, an error floor mitigating turbo encoder receives, asan encoder input, a block of N bits of a systematic data sequence ofdata bits dk. The data sequence dk is fed into a first constituentconvolutional recursive encoder providing first code bits e1 fed into aparity check multiplexer providing the first code bit e1 to a firstencoder delay. While the data sequence dk is being fed into the firstconstituent encoder, the data sequence dk is concurrently fed through asystematic multiplexer communicating the data sequence, designated u andreferred to as systematic data bits that are then fed into a systematicdelay and an encoder interleaver. At the end of the N bits of datasequence dk, a flusher receives an ending state SN from the firstencoder and then the flusher generates m systematic tail bits u*. Theflusher concurrently generates m parity check tail bits e1*. The msystematic tail bits u* are communicated to the systematic multiplexerthat then appends the systematic tail bits u* to the systematic datasequence u. The systematic multiplexer communicates the systematic databits u and systematic tail bits u* to the systematic delay and to anencoder interleaver. The systematic delay communicates both systematicdata bits u and appended systematic tail bits u* to the encoder outputas a block of N systematic data bits u and m systematic tail bits u*.The systematic data output is designated as uk having N+m data and tailbits whereas the original data sequence dk only has N data bits.

As the m systematic tail bits u* are being generated and fed into thesystematic multiplexer, the flusher concurrently generates the m firstparity check bits e1* and communicates the m first parity check bits e1*to the parity check multiplexer which appends the m first parity checktail bits e1* to the code bits e1 and communicates the first code bitse1 and m parity check tail bits e1* as a string of first code bits e1kto the first encoder delay providing a first encoder output e1k as anappended string of first encoder code bits. The entire string of firstcode bits e1k is communicated through the first encoder delay as a blockof N+m first encoder code bits e1k.

As the systematic data sequence string uk=u;u* is fed to the systematicdelay, and as the first encoder string of code bits e1k=e1;e1* is fed tothe first encoder delay, the systematic string uk, consisting of thesystematic data bits u and systematic tail bits u* is concurrently fedto the encoder interleaver. The systematic multiplexer routes the msystematic tail bits u* to the encoder interleaver and to the systematicdelay concurrently as parity check multiplexer routes the parity checktail bits e1* to the first encoder delay. The encoder interleaveroperates upon and interleaves the entire systematic string uk, to thenprovide an interleaved output P(u;u*) after an interleaver time delay.The encoder interleaved output P(u:u*) is fed into the secondconstituent recursive encoder providing an N+m block of second code bitse2k.

The systematic multiplexer communicates the systematic data bit u andappended systematic tail bits u* to the systematic delay for time delay,concurrently as the parity check multiplexer communicates the firstencoder code bits e1 and first parity check tail bits e1* to the firstencoder delay for concurrent time delay, while the encoder interleaverinterleaves systematic data string u;u*. Significantly, the systematictail bits u*, used to emulate the flushing of the first encoder, areinterleaved with the systematic data sequence u without flushing thesecond encoder to the zero state. After the tail bits u* are created atthe end of the flushing process in the first encoder, the entiresystematic sequence string uk=u;u* is interleaved and fed into thesecond encoder. This may lead to the second encoder not terminating atthe all-zero state. In order to avoid carrying any memory over to thenext block, the second encoder is cleared instantaneously aftergenerating the entire sequence of the second parity-check code bit e2k.After interleaving, the encoder interleaver output P(u;u*) is fed intothe second constituent encoder providing an N+m string of second codebits e2k as part of the encoder output. The systematic delay delays thesystematic sequence uk as the first encoder delay delays the firstencoder string e1k, to provide sufficient time for the encoderinterleaver to interleave the systematic data string u;u* and sufficienttime for the second encoder to encode the interleaved output P(u;u*)into the second encoder string of second code bits e2k. The secondencoder output e2k is an interleaved encoded output of an entire N+mblock of second code bits, whereas the systematic output uk consists ofN systematic data bits u and m systematic tail bits u*, and whereas thefirst encoder output e1k consists of N code bits e1 and m parity checktail bits e1*. As such, the first encoder delay and the systematic delayoperate to provide synchronism between the block of N+m bits of thesecond code bits e2k with the block of N+m bits of systematic output ukand with the block of N+m bits of first code bits e1k. Hence, thesystematic data bits uk output consisting of the N systematic data bitsu and m systematic tall bits u*, first encoded output string e1kconsisting of the N first code bits e1 and m parity check tail bits e1*,and the second coded N+m bits e2k output encoded from the encoderinterleaver output P(u;u*) all have the same N+m block length and arecommunicated by the encoder output in synchronism, typically through anoisy channel.

At the end of receiving the input data sequence dk, flushing of thefirst encoder to the zero state is emulated by the flusher generatingthe m systematic tails bits and m first parity check tail bits andresetting the first encoder to the zero state. During the process offlushing, the parity check multiplexer receives the m first parity checktail bits e1* and appends the parity check tail bits e1* to the firstencoder output e1 for the first encoder output ek, as the first encoderis reset to the zero state without the first encoder actually generatingthe parity check tail bits. The systematic tail bits effectivelyemulated flushing tail bits of the first encoder. This emulated flushingoperation, emulates the flushing of the first encoder to the zero state,as if the m systematic m tail bits u* were fed into the first encoderthen being flushed to the zero state while generating the first paritycheck tail bits e1*. This flushing emulation could be, alternatively, ahard wired operation with the flusher communicating the systematic tailbit u* directly into the first encoder then generating the first paritycheck tail bits e1*. However, a practical implementation of the flushermay include a flusher memory look up table, where the ending state SN,read by the flusher, points to the systematic tail bits u* and to thefirst parity check tail bits e1*. As part of the emulated flushingprocess, the first encoder is reset to the zero state which typicallymeans clearing the contents of the shift registers, not shown, with thefirst encoder having a constrain length K, where m equals K-1.

The encoder output provides three blocks of equal N+m length outputsequences uk, e1k, and e2k communicated in time synchronism, with thefirst encoder being flushed to the zero state. However, the secondencoder is not flushed to the zero state, in that, there are no secondencoder flushing tail bits used to flush the second encoder to the zerostate. The second encoder is simply reset to the zero state before thebeginning of the next block of input data dk. The lack of flushing ofthe second encoder affects the operation of the turbo decoder.

Referring to FIG. 2, the input to the first encoder includes Nsystematic data bits u followed by m systematic tail bits u* that arethe flushing bits to terminate the first encoder to the all-zero statein the trellis diagram. Corresponding to this input sequence, the firstencoder generates a first code sequence e1k that consists of N code bitse1 followed by m parity check tail bits e1*. The input to the secondencoder is the interleaved version of the entire N+m bit input sequenceto the first encoder, P(u;u*), including the systematic tailbits u*.Corresponding to this input sequence, the second encoder generates asecond code sequence e2k of length N+m. Because the second encoder needsno flushing, the second encoder trellis path may not terminate at theall-zero state in the trellis diagram. At the end of the encodingprocess, the systematic sequence uk=u;u*, the first encoder codesequence e1k=e1;e1*, and the second encoder code sequence e2k aretransmitted to the noisy channel.

Referring to FIGS. 1 through 4, and particularly the turbo decoder ofFIG. 3, the encoder outputs uk, e1k and e2k are received by the turbodecoder over the noisy channel as respective systematic decoder inputXk, first coded decoder input Y1k and second coded decoder input Y2k.The systematic input Xk and the first coded input Y1k are fed into thefirst a-posteriori probability (APP) decoder. An initial estimate ofbias information indicated by an initialization switch is also fed intothe first APP decoder. The first APP decoder provides a bias estimateoutput that is fed into a first decoder interleaver providing a firstdecoder interleaver output, as the systematic decoder input Xk isconcurrently fed into a second decoder interleaver providing a seconddecoder interleaved output. The second coded input Y2k is fed into a Y2delay matching the processing delay taken by the second decoderinterleaver and providing a delayed Y2k input to the second modifieda-posteriori probability (APP) decoder. The Y2 delay provides for timesynchronism of the inputs to the second modified APP decoder. Initially,the initialization switch is set to zero indicating that the first APPdecoder will use initial bias estimates of the received bits a 50/50middle bias point of being a zero or a one. The channel informationdefines, for example, the shape of a noise probability density functionof a typical receiver demodulator. The second modified APP decoderreceives the first and second decoder interleaver outputs as well as thedelayed second coded decoder input Y2k, all three of which are ininterleaved order. The second APP decoder provides two outputs, onebeing estimates of systematic data bits and the other being an updatedbias information, both in interleaved order. The data bit estimates aresoft data bit estimates. The data bit estimates are deinterleaved by anoutput deinterleaver as the bias information estimates are deinterleavedby a feedback deinterleaver. The data bit estimates and updated biasinformation outputs are generated and deinterleaved once for eachiteration of the turbo decoding process. The data bit estimates are thenfed through a hard limiter which translates the soft data bit estimatesinto zero and one hard data bit values, for each iteration. The hard bitvalues, for each iteration are then stored in a majority selection. Atthe end of the turbo decoding iterations, the majority selection selectseither a zero or a one, for each systematic data bit, depending on thenumber of one and zero vote occurrences acquired during the iterations.In the event of a tie vote occurrences, the bit value of the lastiteration is selected by the majority selection. The majority selectionprovides the decoder output of a block of N systematic data bits Dk.

During each iteration of the turbo decoding, each of the first andsecond APP decoders includes the processes of forward and backwardrecursion. The processes of forward and backward recursions in the APPdecoders trace along the trellis diagram in both the forward andbackward directions while computing state metric values includingforward recursion metrics ak(i), and backward recursion metrics bk(i),for the transmitted systematic data sequence uk passing through state i,where i=0, . . . , 2E(m)-1, at bit index k, where E is the exponentfunction and where k=1, . . . , N+m, based on the received systematicbits Xk, received first code bits Y1k and received second code bits Y2k.The process of forward and backward recursion involves the computationof state metrics having values for each state in the trellis diagramthat includes 2E(m) states for each k bit index. In the trellis diagram,each state is connected with two preceding states and two succeedingstates by two forward and two backward possible connecting branchwords,respectively. Each branchword is defined by the received Xk data bit andcorresponding code bits Y1k or Y2k and extend between states in thetrellis diagram, wherein each state represents the state of the first orsecond encoder defined by respective internal shift registers. Duringthe forward and backward recursion processes, branch metrics arecomputed for each branchword and then state metrics are computed foreach state. Each of the first and second APP decoders perform forwardand backward recursive metric computation. The first APP decoderprovides bias information to the second APP decoder that providesupdated bias information to the first APP decoder through the feed backloop and which provides data bit estimates as well, during eachiteration. During turbo decoding, the bias estimates, updated biasinformation, and data bit estimates are updated for each iteration for apredetermined number of iterations. Each state metric computation isbased upon the preceding branchword metrics and state metrics leading tothe subject state. Each state has a computed metric for each iterationand for each forward or backward recursion. The computed metrics includemetric values for all states over the entire 2E(m)×(N+m) state space andis a function of the channel noise probability density function andupdated bias information, and a function of received data bits Xk andcode bits Y1k or Y2k for respective first and second APP decoders. Thefirst APP decoder computes metric values using the received first codebits Y1k and the second APP decoder computes metric values using thereceived second code bits Y2k. The computed metrics for the entire statespace are computed during forward recursion and then again duringbackward recursion. The computed a-posteriori estimates include biasestimates that are used as the a-priori information for the next APPdecoding operation. After computing the forward and backward statemetrics, the a-posteriori bias estimates and bias information areupdated in the first and second decoders, respectively. The second APPdecoder also updates data bit estimates for majority selection.

Both forward and backward recursions of the first APP decoder start atthe all zero state with a probability of one. However, the forwardrecursion of the second APP decoder may not end in the all zeroterminating state because the second constituent encoder was not flushedby flushing bits to the all zero ending state. The forward recursion ofthe second APP decoder using the N+m second code bits Y2k may terminatein any possible ending state, and hence, the backward recursion in thesecond APP decoder may start from any possible beginning state. Itshould now become apparent that there is no longer a mismatch betweenthe forward recursion ending state and the backward recursion beginningstate in the second modified APP decoder. Particularly, the first APPdecoder forward and backward recursions both begin and end in the allzero state with a probability of one, whereas the second APP decoderforward recursion starts in the all zero state and ends in any possibleending state while the backward recursion begins in any possible statesand ends in the all zero state. And hence, the second APP decoder ismodified to enable the ending of the forward recursion and the beginningof the backward recursion in any possible state, by initializingbackward recursion state metrics to all possible states using endingstate metrics of the forward recursion.

The second APP decoder is modified so that the backward recursion doesnot start at the all-zero state with probability one. Instead, thebackward recursion starts from all possible states i=0, . . . , 2E(m)-1with the same state metrics that the forward recursion terminates,meaning bN+m(i)=aN+m(i) for all states i. Although the APP seconddecoding does not take advantage of the known fact that the sequence e2kcan terminate at the all-zero state, the decoding process enables theforward and backward recursion paths of the highest probabilities tomerge together at the end of the data root portion of the data sequenceXk. Starting the backward recursion from any possible state can reducethe probability of the second APP decoder making decoding errors at theend of the data root portion. There still may be decoding errors at thetail portion in the last m tail bits of a block. However, tail biterrors will not be counted since the tail bits are not part of theactual information data bits.

Referring to FIGS. 3 and 4, the turbo decoding process involves severaliterations. The decoding process starts with a priori initial biasinformation related to an initial estimate of the data bits being zerosor ones. During each iteration, both of the first and second APPdecoders perform a forward recursion followed by a backward recursion.The forward and backward recursions involve the computations of statemetrics typically stored as a table of metric values along a trellisdiagram having a state space matrix of 2E(m) vertical states by N+mhorizontal bits. The first decoder operates on the received systematicdata bits Xk=X;X* and the received first code bits Y1k=Y1;Y1*, executingfirstly a forward recursion and then a backward recursion to generatea-posteriori bias information based on all-zero beginning and endstates. The second decoder operates on the interleaved systematic databits Xk and the received second code bits Y1k, executing firstly aforward recursion and then a backward recursion to generate a-posterioribias information and data bit estimates based on all-zero beginningstate and all possible end states. The first decoder performs forwardand backward recursions from the all zero state with a probability ofone. The modified second APP decoder first generates the forwardrecursion state metric having any ending state values that are then usedto initialize the backward recursion starting from any ending state. Atthe end of the forward recursion, the ending state metric values of allpossible ending states are used to initialize the beginning state metricvalues for all possible beginning states at the beginning of backwardrecursion. After the backward recursion at the end of each iteration,the data bit estimates are subject to hard limiting to zero or one bitvalues for majoring selection voting, and the a-posteriori updated biasinformation are fed back to the first APP decoder for adjusting the databit estimates for the next iteration.

The method of reducing the turbo coding error floor is perfected by notflushing the second encoder and decoding from any possible forwardrecursion ending state and from any possible backward recursionbeginning state. The benefit of not flushing the second encoder is toprovide the second code bits Y2k corresponding to the entire systematicdata string Xk, for improved decoding. As such, there is no mismatch atall between the systematic tail bits and second parity-check tail bitsin tie second APP decoder. The same set of state metrics associated withthe forward recursion termination are used as the initial set of statemetrics for the backward recursion, that is, bN+m(i)=aN+m(i) for allstates i. The second APP decoder is a modified version to theconventional second APP decoder. This modified second APP decoder startsits backward recursion at all 2E(m) possible states, with initialmetrics calculated at the end of the forward recursion for everyiteration. The first APP decoder still starts its backward recursionfrom the all-zero state with probability 1.

The majority selection method is an enhancement to turbo coding. At theend of each iteration, a hard decision is made on each bit based on thedata bit estimates. The final decoded bit is declared to be a one if themajority of the hard decisions on this particular bit from all previousiterations is one, and otherwise is declared to be zero. If there is atie, the current and last hard decision outcome is declared to be thevalue of the decoded bit.

The simulations with the adoption of the error-floor mitigating turbocoding method were performed to illustrate the BER performances of codesfor block sizes of 110, 506 and 1024 with constraint lengths of 3, 4 and5. Significantly, the BER performances do not merge with the analyticaltransfer function bounds. Instead, the simulated BER performance curvescontinue to drop beyond the analytical transfer function bound whichindicating that no error floor exists down to the BER range of 1×10E-8.A feature of the method is that the increase of the constraint lengthdoes not improve the performance significantly for short block size. Itis well known that increasing the constraint length will increase thedecoder complexity exponentially. However, a code with a constraintlength of 3 is adequate for block size of about 100 data bits. As theblock size increases to the vicinity of 500, the use of the code with aconstraint length of 4 can gain 1 dB above the code with a constraintlength of 3 at a BER of 1×10E-6. However, using the code with aconstraint length of 5 does not significantly further improve the codinggain. When the block size increases to 1000, a code with a constraintlength of 5 can provide an additional 0.7 dB coding gain over the codewith a constraint length of 4. These results indicate that increasingthe constraint length dues not necessarily provide significant codinggain. Hence, for short block size, such as 100, a constraint length of 3is adequate, and block sizes greater than 1000, codes with a constraintlength of 5 is effective.

The tail effects between the systematic and parity-check tail sequencesdue to flushing the second constituent encoder are eliminated by theerror-floor mitigating turbo coding method. The method not only improvesthe BER performance, but also removes the error floor for turbo coding.To achieve a specific BER, utilizing the method can reduce the number ofdecoding iterations, resulting in a shorter decoding delay. The methodincludes features such as ending the forward and beginning the backwardrecursion for the second decoding at any possible state, not flushingthe second encoder, using a block wise interleaved input into the seconddecoder, and majority selection, to reduce the turbo code error floor.

Referring to FIGS. 5 through 8, the repetitive turbo coding aspect ofthe invention has unique features of encoding bit partition anddeletion. The encoder bit partitioning uses a repetition rate rrepeating the systematic sequence data bits prior to encoding. Arepetitive turbo encoder for turbo coding uses encoder bit partitioningwith a repetitive turbo decoder having a corresponding bit deletionfunction as a new turbo code repetitive structure, referred to asrepetitive turbo coding. Repetitive turbo codes may be used for variouscode rates and constraint length encoders. For some code configurations,the repetitive structure can further increase the coding gain byapproximately 1 dB asymptotically over conventional turbo coding. Therepetitive turbo coding method can be used with optional encoderpuncturing and decoder bit insertion process for decreasing the requiredtransmission bandwidth.

The second interleaver for the second encoder is an essential device forthe turbo code structure. After selecting a specific interleavingpattern, the turbo code BER performance is dominant by the error eventscreated by a particular bit pattern in the systematic sequence thatgenerates the minimum Hamming weight turbo codeword. With the use ofrepetitive encoding using the bit partitioning, the benefit is toprevent this particular bit pattern from happening in the inputsequences to the constituent encoders. Therefore, the minimum Hammingdistance of the repetitive turbo code is increased and the BERperformance is improved.

Referring particularly to FIG. 5, the encoder input of one block of Nbits dk is partitioned by a bit partitioner using a rate of r, in whicheach input bit is simply divided into r output bits during each inputbit time interval. As each bit of the input block is received, the bitis duplicated r times, each of which takes 1/r input bit time. Theencoder may operate at a r-times faster clock rate. After the repetitiveturbo encoder partitions the entire systematic input block dk, theflusher generates m systematic tail bits u* as an appendage to therepetitive systematic root sequence ru. The flushing tail bits u*depends upon the state of the first encoder at the end of encoding theroot portion P1(ru) of the first encoder input sequence. Preferably, them tail bits are routed to both first and second encoders but the flushermay optimally route different m tail bits to the second encoder. Thesystematic sequence uk=ru;u*, which consists of rN+m bits, iscommunicated to the second encoder interleaver. The repetitivesystematic sequence uk=ru;u* may also be communicated to an optionalsystematic interleaver and to an optional first encoder interleaver.When a systematic interleaver is used, an rN+m sized interleaving outputPS(ru;u*) is generated and communicated to the systematic delay. Whenthe first encoder interleaver is used, an rN sized interleaved outputP1(ru) is generated. The first encoder interleaver permutes the rootportion ru of the repetitive systematic sequence. The tail bits u* areappended to generate an rN+m bit first encoder input P1(ru);u*communicated to the first encoder providing the first encoder outpute1(ru);e1*. In one form of the invention, the second encoder interleaveroperates a rN+m sized interleaving pattern P2(ru;u*) on the entiresystematic string ru;u*, generating a second interleaved outputP2(ru;u*) fed into the second encoder providing the second encoderoutput e2(ru;u*). Preferably, the tail bits u* are used in both thefirst and second encoders enabling the use of the error-floor mitigatingturbo coding method. In another form of invention, the second encoderinterleaver performs exactly the same operation as the first encoderinterleaver except using a different rN sized interleaving pattern P2.In this case, the second encoder interleaver output P2(ru;u*) is in theform of P2(ru);u* and the second encoder output e2(ru;u*) is in the formof e2(ru);e2*, with u* and e2* located at the tail portions of therespective data structures P2(ru) and e2(ru).

The repetitive turbo encoder relies upon repeating every bit of theinformation sequence dk. The repeated sequence must enter into thesecond encoder interleaver and may enter into the optional first encoderinterleaver. The interleaving patterns of these two interleavers must bedifferent and independent. This dual structure retains the independencebetween two code sequences e1 and e2. The two interleaved sequences arerespectively fed into the two constituent first and second encoders. Thedelayed systematic string ru;u* and first and second encoder outputse1(ru;u*) and e2(ru;u*) may be fed into a puncture pattern that, in oneembodiment, deletes the replicated bits in the root portion of thesystematic string ru;u*, reducing the total number of systematic bitsfrom rN+m to N+m. In other embodiments, the puncture pattern maypuncture at a variety of rates and in a variety of patterns on thesystematic, first encoder and second encoder output strings. Forexample, in one embodiment, in addition to the systematic output stringuk being punctured to u;u*, the puncture pattern for e1(ru;u*) ande2(ru;u*) sequences may also be the same bit deletion puncture pattern,retaining the same code rate of 1/3, but other puncture patterns may beused. Interleavers and puncture patterns are well known by those skilledin the art. The punctured outputs uk, e1k, and e2k are the turbo encoderoutputs of three blocks of possibly different sizes communicated overthe noisy channel. A first encoder delay and a systematic delay providesynchronism among the first encoder, second encoder and systematicsequences.

Referring to FIG. 6, in one embodiment, neither the systematicinterleaver nor the first encoder interleaver is used. The secondencoder interleaver operates a rN sized interleaver P2 on the root inputsequence ru and appends the flushing tail bits u*, providing aninterleaved output in the form of P2(ru);u* to the second encoder. Thepuncture pattern only deletes the replicated bits in the systematic rootsequence ru retaining the original input sequence u appended by thesystematic tail bits u*, forming the systematic output string uk=u;u*.The composite turbo encoder output to the noisy channel is representedby {uk,e1k,e2k}. The total number of transmitted channel bitscorresponding to a block of N encoder input bits is (2r+1)N+3m.

The repetitive turbo first and second encoder provide a code rate thatis lower than a conventional turbo encode without puncturing. It shouldbe apparent that the repeated systematic bits need not be transmittedover the channel, and the simple 1/r puncturing increases the code rate.Without the 1/r puncturing the first and second code bits e1k and e2k,the code rate becomes a rate 1/(2r+1) when N is much greater than m.Using the same rate of reduction in encoded bit, the puncture patternprovides a code rate of 1/3. Various puncturing patterns can be used,but a puncturing pattern providing a 1/r code rate is preferred in someapplications.

With the use of bit repetition in the repetitive turbo encoder, thebenefit is to prevent the generation of a particular bit patternproviding the nonrepetitive turbo codeword with the smallest Hammingdistance, and therefore increases the Hamming distance. There is abenefit of interleaving the systematic sequence as an input to the firstencoder is to create a more random sequence into the first encoder,subject to the non-generation of a bit pattern providing thenonrepetitive smallest Hamming distance, resulting in an increase in theHamming distance for improved turbo decoding. However, there is aninsignificant improvement in the decoding process by interleaving andtransmitting an interleaved version of the systematic sequence [uk],instead of simply transmitting the systematic sequence uk. Hence, thesystematic interleaver for the systematic channel uk does not offersignificant coding gain, whereas the use of the first encoderinterleaver does provide marginal increase in the coding gain, whenusing repetitive bit partitioning. The second encoder interleaver is anessential device for the repetitive turbo coding. The benefit of usingthe second encoder interleaver is to generate a different input sequenceto the second encoder from that to the first encoder resulting in alarger minimum Hamming distance. Hence, bit partitioning in combinationwith both first and second interleaving increases the minimum Hammingdistance resulting in improved coding gain. Repeatedly feeding each andevery information bit more than once into the encoders is a preferredmeans for increasing the coding gain.

Referring to FIGS. 5 through 8, and particularly the turbo decoder ofFIGS. 7, the encoder outputs uk, e1k and e2k are received by the turbodecoder over the noisy channel as respective systematic decoder inputxk, first coded decoder input y1k and second coded decoder input y2k,which are fed into the bit insertion providing the Xk, Y1k, and Y2ksequences each of length rN+m. The bit insertion function is an inversefunction of the selected puncture pattern. The bit insertioncorresponding to the puncture deleting the replicated systematic bits ruis to duplicate the received symbols in the systematic fragment, whilethe bit insertion corresponding to the puncture deleting the systematictail bits u*, if any though not suggested, and coded bits e1(ru);e1* ande2(ru;u*) is to insert the dummy signal, zero value, at the properpositions. The resulting sequences Xk, Y1k, and Y2k strings retain theiroriginal lengths rN+m used in the encoder for processing by the firstand second APP decoders. The turbo decoder may also operate at anr-times faster clock rate. The X deinterleaver provides an inversefunction of the encoder systematic interleaver, when used. Likewise, theY1 deinterleaver provides an inverse function of the first encoderinterleaver when used. After bit insertion and Y1 and X deinterleaving,when used, the systematic input Xk and the first coded input Y1k are fedinto the first a-posteriori probability (APP) decoder. The lengths ofthese inputs are rN+m. The X delay, Y1 delay, Y2 first delay and Y2second delay provide synchronism of the three sequences Y1k, Y2k and Xkat inputs to the first and second APP decoder. An initial estimate ofbias information indicated by an initialization switch is also fed intothe first APP decoder. The first APP decoder provides the bias estimatethat is fed into a first decoder interleaver providing a first decoderinterleaver output, as the systematic decoder input Xk is concurrentlyfed into a second decoder interleaver providing a second decoderinterleaved output. The second coded input Y2k is fed into a secondmodified a-posteriori probability (APP) decoder. A Y2 delay provides fortime synchronism. These interleaving and deinterleaving patterns need tobe properly designed so that all inputs to the first or second decoderare in the same respective order P1 and P2 as used in the respectivefirst and second constituent encoders. Initially, the initializationswitch is set to zero indicating that the first APP decoder will useinitial bias estimates of the received bits a 50/50 middle bias point ofbeing a zero or a one. The channel information defines, for example, theshape of a noise probability density function of a typical receiverdemodulator. The second modified APP decoder receives the first andsecond decoder interleaver outputs as well as the second coded decoderinput Y2k, all three of which are in interleaved order used by thesecond constituent encoder. The second APP decoder provides two outputs,one being systematic data bits estimates and the other being updatedbias information. The data bit estimates are soft data bit estimates.The data bit estimates are deinterleaved by an output deinterleaver intothe order of uninterleaved encoder systematic sequence ru;u* as theupdated bias information is deinterleaved by a feedback deinterleaverinto the order of P1 used by the first constituent encoder. In the casethat the second constituent encoder is also flushed to the all-zerostate, either the conventional or modified second APP decoder can beused. The data bit estimates and bias information outputs are generatedand deinterleaved once for each iteration of the turbo decoding process.The data bit estimates are then fed through a hard limiter thattranslates the soft data bit estimates into zero and one hard data bitvalues, for each iteration. The hard bit values, for each iteration, foreach duplicated bit, are then stored in a majority selection. At the endof the turbo decoding iterations, the majority selection selects eithera zero or a one, for each repetitive systematic data bit, depending onthe number of one and zero vote occurrences acquired during theiterations. At the end of the interaction, the second majority selectionstarts to select either a zero or a one for each decoded bit by majorvote among r replicated bits, depending on the number of one and zerovote occurrences among all r duplicated bits, thereby deletingrepetitive bits as an inverse function of the bit partitioningrepetition. In the event of a tie vote occurrences, the major vote ofthe last iteration is selected or simply select either a one or a zero.The majority selection provides the decoder output of a block of Nsystematic data bits Dk.

Referring to FIG. 8, as an inverse operation on the data structure givenby FIG. 6, after the receipt of {xk, y1k, y2k}, the repetitive turbodecoder first repeats the systematic bits xk by r times and then feedsthe resulting sequences to a conventional turbo decoder. The decodingalgorithm preferably provides bit insertion to provide an inversefunction of the puncture pattern. Majority selection bit also providesvoting bit deletion as an inverse function of the bit partitioningfunction. The bit insertion function may be simple duplication of thereceived symbols in the systematic fragment or the insertion of zero bitvalue signal at the deleted positions of the codeword, feeding theresulting sequences into a conventional nonrepetitive turbo decoder at aclock rate of r time faster. After the decoding, a majority selectionfunction is used for final decision as to whether a bit is declared tobe a zero or a one, and for the bit deletion function.

It should now become apparent that the repetitive turbo encoder decodersystem can have a variety of configurations, so long as the systematicsequence is repeated and enters into a rN or rN+m sized encoderinterleaver providing an interleaved input to a respective one of theconstituent encoders. A first exemplar configuration is where Xk has aninput systematic symbol length of N+m with r repetition and 1/rpuncturing with 1/r bit insertion, where Y1k has a input code symbollength of rN+m with r repetition, and where Y2k has an arbitrary inputcode symbol length with input encoder interleaving, and puncturing, anddecoder bit insertion and deinterleaving, so that three rN+m sizesrepetitive sequences are processed in the decoder with a majorityselection bit deletion. A second exemplar configuration is where Xk hasan input systematic symbol length of N+m with r repetition and 1/rpuncturing with 1/r bit insertion, where Y1k has a input code symbollength of rN+m with encoder interleaving and decoder deinterleaving, andY2k has an arbitrary input code symbol length with input encoderinterleaving, puncturing, and decoder bit insertion and deinterleaving,so that M three rN+m sized repetitive sequences are processed in thedecoder with majority selection bit deletion. A third exemplarconfiguration is where Xk has an input systematic symbol length of N+mwith r repetition and 1/r puncturing and bit insertion, where Y1k has anarbitrary input code symbol length with input encoder interleaving andpuncturing, and decoder bit insertion and deinterleaving, and where Y2khas an arbitrary input code symbol length with input encoderinterleaving, puncturing and bit insertion and decoder deinterleaving,so that three rN+m sized repetitive sequences are processed in thedecoder with majority selection bit deletion. There are of course, manypossible configurations. For example, the decoder received sequence xk,y1, and y2 need not necessarily have the same transmitted symbol length,and the x and y1 sequences need not be encoder interleaved and decoderdeinterleaved. What is required is that at least one of the constituentencoder sequences have an interleaved repetitive input, for exampleP2(ru). Generally, it is necessary that one encoder sequence Y1 or Y2 berepetitive and interleaved prior to encoding, and it is preferred thatthe decoder operate on rN+m bits as a repetitive decoder.

The repetitive turbo coding system comprising the repetitive turboencoder and decoder can also operate as an error-floor mitigating turbocoding system, by not flushing the second encoder to the all zero stateand using the modified second APP decoder. In such cases, the turbocoding system has coding gain contribution from both the interleavedrepetitive second encoding and the nonflushing of the second encoderusing the modified second APP decoder for forward recursions ending andthe backward recursion beginning at any state. When the interleavedflushing m tail bits to the second encoder do not set the second encoderto the zero state at the end of the entire systematic sequence, then amodified APP second encoder can be used for improved coding gain. Also,where multiple encoder interleavers are used, such as both the first andsecond encoder interleaver, the first and second decoder interleaverfunctions need to be formed as hybrid interleavers so as to correspondto the dual interleaver configuration. Those skilled in the art of turbocoding can configure hybrid decoder interleavers for proper decodingwhen using multiple encoder interleavers.

For repetition of a rate r=2, the majority selection does not provide acoding gain and the BER performance will be degraded due to the decreaseof the code rate. However, for a repetition rate of r=3, the analyticalBER is given by Pb=pE3+3pE2(1-p) where p is computed from the Pbsummation equation with Es being Eb/7. The BER for a repetition rate ofr=3 can be examined for optimizing the code structure. The followingsimulated PERFORMANCE TABLE lists the best repetitive code for r=3 andfor K=3, K=4, and K=5. The values of Pb are evaluated for the transferfunction bound with an Eb/N0=8 dB and a block size of 250.

    ______________________________________                                        REPETITIVE CODE PERFORMANCE TABLE                                             g0             g1      Pb                                                     ______________________________________                                        K = 3                                                                         111            101     4.31E-13                                               101            111     2.91E-11                                               111            110     4.06E-10                                               111            100     4.50E-10                                               101            110     3.04E-09                                               110            111     3.58E-09                                               101            100     1.29E-07                                               K = 4                                                                         1011 1111 1.19E-15                                                            1101 1111 1.19E-15                                                            1011 1101 5.57E-15                                                            1101 1011 5.57E-15                                                            1011 1001 2.49E-14                                                            1101 1001 2.49E-14                                                            1111 1011 1.73E-13                                                            1111 1101 1.73E-13                                                            1001 1111 1.75E-13                                                            1111 1001 1.98E-13                                                            K = 5                                                                         10011 11101 1.77E-17                                                          11001 10111 1.77E-17                                                          10011 11011 2.20E-17                                                          11001 11011 2.20E-17                                                          10011 11111 3.05E-17                                                          11001 11111 3.05E-17                                                          10111 11101 7.24E-17                                                          11101 10111 1.24E-17                                                          11111 10101 8.15E-17                                                          10111 10001 9.48E-17                                                          ______________________________________                                    

The BER performance of the codes listed in the BER PERFORMANCE TABLEwith repetition rate of r=3 are compared to using a block size of 500.The repetitive turbo code with a repetition rate of r=3 canapproximately achieve an additional 1 dB of coding gain asymptoticallyfor a constraint length of K=5 with a block size of N=500. BERperformances can be compared against prior preferred nonrepetitive turbocodes of the same rates by using low rate constituent encoder. Forconstraint lengths of K=4 and K=5, the repetitive turbo code with arepetition rate of r=3 and resulting code rate of 1/7 can improve theBER by two orders of magnitude over those using a code rate of 1/4constituent code with a block size of 1000. The smaller the block size,the less significant the improvement. The analytical BER bounds forrepetitive turbo codes of constraint lengths of K=3, K=4, and K=5 showthe improved performance over the nonrepetitive turbo code. Because theanalytical BER bound at high Eb/N0 can be used as the asymptotic BERperformance of the turbo code and as a referencing location of the errorfloor, this means that the error floor of the turbo code can be furtherreduced by adopting a repetitive structure.

It should be apparent, the repetitive turbo coding system and method canfunction in a variety of configurations and can be combined and enhancedwith mitigated turbo coding. Those skilled in the art can makeenhancements, improvements and modifications to enhance the invention.However, those enhancements, improvements and modifications maynonetheless fall within the spirit and scope of the following claims.

What is claimed:
 1. A method for communicating systematic data bitsusing a prior bias information over a channel, the method comprising thesteps of,generating an input block of data bits as the systematic databits, repeating r time the systematic data bits as a repetitivesystematic sequence, generating systematic tail bits, appending thesystematic tail bits to the repetitive systematic sequence providing asystematic string, first data bit encoding the repetitive systematicsequence into first code bits, first tail bit encoding the systematictail bits into first parity check tail bits, the first encoding steptransits between defined states ending in an all zero state, appendingthe first parity check tail bits to the first code bits providing afirst code string, second encoder interleaving the systematic stringproviding a second encoder interleaved string, second encoding thesecond encoder interleaved string into a second code string ininterleaved order, the second code string, the first code string and thesystematic string have equal length, the second encoding step transitsbetween defined states not ending in an all zero state, transmitting thesystematic string, the first code string and the second code stringthroughout the channel, receiving the second code string, the first codestring, and the systematic string, first decoding the systematic stringusing the first code string and using the a priori bias information asbias information as a first a posteriori probability bias estimationproviding a bias estimate, first decoder interleaving the bias estimateinto an interleaved bias string, second decoder interleaving thesystematic string into a decoder interleaved string, second decoding thedecoder interleaved string using the interleaved bias string and thesecond code string providing interleaved updated bias information andinterleaved data bit estimates, feed back deinterleaving the interleavedupdated bias information into updated bias information, feeding back theupdated bias information as the a-priori bias information for firstdecoding step, output deinterleaving the interleaved data bit estimatesinto data bit estimates, hard limiting the data bit estimates intovalues of zero and one, repeating the first decoding, first decodinginterleaving second decoding interleaving, second decoding, feed backdeinterleaving, feeding back, output deinterleaving and hard limitingsteps a plurality of iterations for generating a repetitive output blockof values as an estimate of the repetitive systematic sequence, and bitdeleting 1/r times the repetitive output block of values into an outputblock of values as an estimate of the input block of data bits.
 2. Themethod of claim 1 further comprising the steps ofmajority selecting theoutput block of values for each of the data bits based on occurrences ofzero or one values generated during the plurality of iterations togenerate an output block of data bits as an estimate of the input blockof data bits.
 3. The method of claim 1 further comprising the stepsof,puncturing the second code string prior to transmission, bitinserting the second code string after transmission, the bit insertingfunction is an inverse function of the puncturing step.